3.4相互独立的随机变量例1 对于第一节例2中的随机变量 X和Y,由于[2e-2xx>0,e-, y>ofx(x) =fr(y) =其他,其他，0,0,得f(x,y) = fx(x)fy(y),因而X和Y是相互独立的K
例1 对于第一节例2中的随机变量 X和Y， 由于 f (x) X = 2 , 0, 2 − e x x 0, 其他， f ( y) Y = , 0, − e y y 0, 其他， f (x, y) f (x) f ( y), = X Y 因而X和Y是相互独立的. 得
3.4相互独立的随机变量例2若X,Y具有联合分布率XP(Y = j)01Y2/61/211/62/61/221/6Plx=i12/31/3则有 P(X = 0,Y =1)= 1/6 = P[X = 0)P[Y = 1),P(X = 0,Y = 2)= 1/6 =P(X = 0)P(Y = 2)}P(X =1,Y =1) = 2/6 = P[X = 1)P(Y = 1),P[X =1,Y = 2)= 2/6 = P(X =1)P(Y = 2},K
X Y 1 2 0 1 1 6 2 6 1 6 2 6 Px = i 1 3 2 3 PY = j 1 2 1 2 1 例2 若X,Y具有联合分布率 则有 P{X = 0,Y = 1} = 1 6 = P{X = 0}P{Y = 1}, P{X = 0,Y = 2}= 1 6 = P{X = 0}P{Y = 2}, P{X = 1,Y = 1} = 2 6 = P{X = 1}P{Y = 1}, P{X = 1,Y = 2}= 2 6 = P{X = 1}P{Y = 2}